Flow of viscous fluids through a porous deformable matrix

Morland, Leslie

doi:10.1007/bf02125770

Cited by 60 publications

(73 citation statements)

References 20 publications

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“…Morland (1992) showed that the partial and intrinsic densities are related by a linear volume fraction scaling, while the partial and intrinsic velocity fields are identical, i.e. 2.2.…”

Section: Governing Equationsmentioning

confidence: 99%

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Particle-size segregation and diffusive remixing in shallow granular avalanches

2006

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Segregation and mixing of dissimilar grains is a problem in many industrial and pharmaceutical processes, as well as in hazardous geophysical flows, where the sizedistribution can have a major impact on the local rheology and the overall run-out. In this paper, a simple binary mixture theory is used to formulate a model for particlesize segregation and diffusive remixing of large and small particles in shallow gravitydriven free-surface flows. This builds on a recent theory for the process of kinetic sieving, which is the dominant mechanism for segregation in granular avalanches provided the density-ratio and the size-ratio of the particles are not too large. The resulting nonlinear parabolic segregation-remixing equation reduces to a quasi-linear hyperbolic equation in the no-remixing limit. It assumes that the bulk velocity is incompressible and that the bulk pressure is lithostatic, making it compatible with most theories used to compute the motion of shallow granular free-surface flows. In steady-state, the segregation-remixing equation reduces to a logistic type equation and the 'S'-shaped solutions are in very good agreement with existing particle dynamics simulations for both size and density segregation. Laterally uniform time-dependent solutions are constructed by mapping the segregation-remixing equation to Burgers equation and using the Cole-Hopf transformation to linearize the problem. It is then shown how solutions for arbitrary initial conditions can be constructed using standard methods. Three examples are investigated in which the initial concentration is (i) homogeneous, (ii) reverse graded with the coarse grains above the fines, and, (iii) normally graded with the fines above the coarse grains. Time-dependent twodimensional solutions are also constructed for plug-flow in a semi-infinite chute.

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“…Morland (1992) showed that the partial and intrinsic densities are related by a linear volume fraction scaling, while the partial and intrinsic velocity fields are identical, i.e. 2.2.…”

Section: Governing Equationsmentioning

confidence: 99%

“…These terms are retained in the current model and an additional remixing force −ρd∇φ µ (e.g. Bear 1972;Morland 1992) is added, that seeks to drive grains of phase ν towards areas of lower concentration. The interaction drag is therefore…”

Section: Governing Equationsmentioning

confidence: 99%

Particle-size segregation and diffusive remixing in shallow granular avalanches

2006

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“…A three constituent continuum mixture theory (e.g. Truesdell 1984, Morland 1992 is therefore used to model the system, which assumes that every point is simultaneously occupied by all three phases. This allows overlapping partial density ρ ν , partial velocity u ν and partial pressure p ν fields to be defined for each constituent ν.…”

Section: Mixture Frameworkmentioning

confidence: 99%

“…or physical, variables, which are measurable. Morland (1992) showed that the partial velocity and density are related to their intrinsic counterparts by 9) where the superscript * denotes an intrinsic variable. However, the partial and intrinsic pressure can be related by any functional relation, so long as (2.4) is not violated.…”

Section: Mixture Frameworkmentioning

confidence: 99%

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A three-phase mixture theory for particle size segregation in shallow granular free-surface flows

2006

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Particle-size segregation within granular materials is of great technological significance yet it is still very poorly understood. There are several causes for segregation, but this paper focuses on kinetic sieving which is the dominant mechanism in dense gravity-driven shallow free-surface flows, or, granular avalanches. The segregation model is derived from a three-phase mixture theory composed of large particles, small particles and a passive interstitial fluid. Steady-state solutions are constructed for a normally graded inflow in a steady uniform flow field. This problem is of fundamental interest, because it shows how an unstably stratified layer readjusts into a stable configuration. Expansion fans and concentration shocks are generated and sufficiently far downstream inversely-graded segregated layers form, with the larger particles overlying the finer ones. The distance for complete segregation to occur is shown to increase with rising fluid density and tends to infinity as its density approaches that of the grains. If the particles are buoyant then the initial configuration is stable. An exact time-dependent two-dimensional solution is constructed for plug-flow, which exploits the uncoupling of material columns of grains in the absence of shear. This yields insight into the nature of more complex numerical solutions for strong shear, which are computed with a high resolution, shock-capturing numerical scheme.

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Uni-axial wave propagation and pore pressure generation in fluid saturated sands exhibiting irreversible compaction

Morland

Staroszczyk

1998

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYThe propagation of a plane load-unload pulse through a compacting sand is analysed and illustrated for both dry sand and liquid saturated sand in undrained conditions. A major feature is the interaction between the initial loading wave and the faster following unloading wave. Free draining and undrained conditions exhibit distinct qualitative and quantitative results, and the pore liquid pressure generation is a significant physical feature. Illustrations show the effects of different applied surface pulse shapes.1998 John Wiley & Sons, Ltd.

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Flow of viscous fluids through a porous deformable matrix

Cited by 60 publications

References 20 publications

Particle-size segregation and diffusive remixing in shallow granular avalanches

Particle-size segregation and diffusive remixing in shallow granular avalanches

A three-phase mixture theory for particle size segregation in shallow granular free-surface flows

Uni-axial wave propagation and pore pressure generation in fluid saturated sands exhibiting irreversible compaction

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